(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Simplify the following :

`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`

Simplify the following :

`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`

If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.

In the following, find the values of a and b.

`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`

In the following, find the values of a and b:

`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`

In the following, find the values of a and b:

`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`

In the following, find the values of a and b:

`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`

In the following, find the values of a and b:

`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`

In the following, find the values of a and b:

`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`

In the following, find the values of a and b:

`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`

In the following, find the values of a and b:

`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`

In the following, find the value of a and b:

`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`

In the following, find the value of a and b:

`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`

If x = `(7 + 4sqrt(3))`, find the value of

`sqrt(x) + (1)/(sqrt(x)`

If x = `(7 + 4sqrt(3))`, find the value of

`x^2 + (1)/x^2`

If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.

If x = `(7 + 4sqrt(3))`, find the values of :

`(x + (1)/x)^2`

If x = `(4 - sqrt(15))`, find the values of 

`(1)/x`

If x = `(4 - sqrt(15))`, find the values of

`x + (1)/x`

If x = `(4 - sqrt(15))`, find the values of 

`x^2 + (1)/x^2`